I'm puzzled by these figures. How does UK get 4? London and Birmingham, yes. Manchester if you consider all the satellite towns. Nothing else in truth is over one million, let alone two. If you consider greater Glasgow then World population review puts it as high as 1.6 million but no more. Nothing else comes remotely near that figure.
According to citypopulation.de, the fourth city would be Leeds with 2.15 million. To be fair, I'm not super familiar with the methodology used by the site, since a lot of the figures seem to be pretty generous with their definition of urban agglomeration.